{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is the price of FX forward =  1.041868932038835\n",
      "What is the Value of FX forward after 180 =  0.04701510904641015\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def PriceFXForward(S0, Rdc,Rfc,T):\n",
    "    # Pricing FX forward\n",
    "    F=S0*(((1+Rdc)/(1+Rfc))**(T/365))\n",
    "    return F\n",
    "\n",
    "def ValueFXForward(St, F, Rdc,Rfc,T,t ):\n",
    "    # valuation of Vt(F0:T)\n",
    "    Val=St/((1+Rfc)**((T-t)/365))-F/((1+Rdc)**((T-t)/365))\n",
    "    return Val\n",
    "\n",
    "#main function\n",
    "Rdc=1/100\n",
    "Rfc=3/100\n",
    "T=365\n",
    "S0=1.0625\n",
    "#Pricing FX forward \n",
    "\n",
    "F= PriceFXForward(S0, Rdc,Rfc,T)\n",
    "#After 180 days, valuing Vt(F0:T)\n",
    "t=180\n",
    "St=1.1\n",
    "Val= ValueFXForward(St, F, Rdc,Rfc,T,t)\n",
    "print('What is the price of FX forward = ',F)\n",
    "print(\"What is the Value of FX forward after %d = \" %(t),Val)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We earn profit= 36.96470588235301 DC\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def PriceFXForward(S0, Rdc,Rfc,T):\n",
    "    # Pricing FX forward\n",
    "    F=S0*(((1+Rdc)/(1+Rfc))**(T/365))\n",
    "    return F\n",
    "\n",
    "def CoveredIntArbitrage(S0,Fmkt,Rdc,Rfc,T):\n",
    "# input: S0, spot rate\n",
    "#           Fmkt, FX forward market price\n",
    "#           Rdc, Domestic interest rate\n",
    "#           Rfc, Foreign interest rate\n",
    "#           T, the maturity of FX forward\n",
    "#output: prof, profit investor earned\n",
    "#            initial_currency: Initially, the currency investor should\n",
    "#            lend from bank\n",
    "    F=PriceFXForward(S0, Rdc,Rfc,T);\n",
    "    if (F<Fmkt):\n",
    "        prof =1000*((Fmkt/S0)*(1+Rfc)**(T/365)-(1+Rdc)**(T/365))\n",
    "        initial_currency='DC'\n",
    "    else:\n",
    "        prof =1000*((S0/Fmkt)*(1+Rdc)**(T/365)-(1+Rfc)**(T/365))\n",
    "        initial_currency='FC'\n",
    "\n",
    "    return prof, initial_currency\n",
    "\n",
    "Rdc=1/100;\n",
    "Rfc=3/100;\n",
    "T=365;\n",
    "S0=1.0625;\n",
    "Fmkt=1.0800;\n",
    " \n",
    "prof,initial_currency=CoveredIntArbitrage(S0,Fmkt,Rdc,Rfc,T)\n",
    "\n",
    "print('We earn profit=',prof,initial_currency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlUAAAHiCAYAAADBITniAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x268418cc6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def european_opt_payoff(typ,S, K):\n",
    "#typ =\"type\" when \"c\"=call, \"p=put\"\n",
    "    if (typ=='c'):\n",
    "        payoff=(abs(S-K)+(S-K))/2\n",
    "    else:\n",
    "        payoff=(abs(K-S)+(K-S))/2\n",
    "    \n",
    "    return payoff\n",
    "\n",
    "S=np.arange(1,10,0.01) #underlying asset prices\n",
    "K=5.0 #strike price\n",
    "typ='c'\n",
    "pay_off_c= european_opt_payoff(typ,S, K)\n",
    " \n",
    "typ='p'\n",
    "pay_off_p= european_opt_payoff(typ,S, K)\n",
    "\n",
    "#xmin=min(S)\n",
    "#xmax=max(S)\n",
    "#ymin=min(-pay_off_c)\n",
    "#ymax=max(pay_off_c)\n",
    "\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.subplot(2,2,1)\n",
    "#plt.axis([xmin,xmax,ymin,ymax])\n",
    "plt.axhline(0, color='black', lw=2)\n",
    "plt.plot(S,pay_off_c,color = '#1B9E77', linewidth=1.5)\n",
    "plt.title('Long a Call')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.subplot(2,2,3)\n",
    "plt.axhline(0, color='black', lw=2)\n",
    "plt.plot(S,-pay_off_c,color = '#1B9E77', linewidth=1.5)\n",
    "plt.title('Long a Call')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.subplot(2,2,2)\n",
    "plt.axhline(0, color='black', lw=2)\n",
    "plt.plot(S,pay_off_p,color = '#1B9E77', linewidth=1.5)\n",
    "plt.title('Long a Put')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.subplot(2,2,4)\n",
    "plt.axhline(0, color='black', lw=2)\n",
    "plt.plot(S,-pay_off_p,color = '#1B9E77', linewidth=1.5)\n",
    "plt.title('Short a Put')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Anaconda3]",
   "language": "python",
   "name": "Python [Anaconda3]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
